Functional Characterization and Topological Modularity of Molecular Interaction Networks

Transcription

1 Functional Characterization and Topological Modularity of Molecular Interaction Networks Jayesh Pandey 1 Mehmet Koyutürk 2 Ananth Grama 1 1 Department of Computer Science Purdue University 2 Department of Electrical Engineering & Computer Science Case Western Reserve University Asia Pacific Bioinformatics Conference, 2010

2 Molecular Interaction Networks Provides a high level description of cellular organization Directed and undirected graph representation Nodes represent cellular components Protein, gene, enzyme, metabolite Edges represent reactions or interactions Binding, regulation, modification, complex membership, substrate-product relationship S.cerevisiae Protein-Protein Interaction (PPI) Network

3 Function : Gene Ontology Molecular annotation provides a unified understanding of the underlying principles Gene Ontology: A controlled vocabulary of molecular functions, biological processes, and cellular components Terms (concepts) related by is-a, part-of relationships If a molecule is annotated by a term, then it is also annotated by terms on the paths towards root.

4 Function & Topology in Molecular Networks How does function relate to network topology?

5 Functional Coherence in Networks Modularity manifests itself in terms of high connectivity in the network Functional association (similarity) is correlated with network proximity A measure for annotation proximity of nodes (semantic similarity) A measure for network distance Sharan et al., MSB, 2007

6 Assessing Functional Similarity Gene Ontology (GO) provides a hierarchical taxonomy of biological process, molecular function and cellular component Assessment of semantic similarity between concepts in a hierarchical taxonomy is well studied (Resnik, IJCAI, 1995)

7 Semantic Similarity of GO Terms Resnik s measure based on information content I(c) = log 2 ( G c / G r ) δ I (c i, c j ) = max c A i A j I(c) G c : Set of molecules that are associated with term c, r: Root term A i : Ancestors of term c i in the hierarchy λ(c i, c j ) = argmax c Ai A j I(c): Lowest common ancestor of c i and c j Resnik(c 3, c 4 ) = Max(IC(c 1 ), IC(c 2 ))

8 Functional Similarity of Molecules Each molecule (protein or domain) is associated with multiple GO terms Average (Lord et al., Bioinformatics, 2003) ρ A (S i, S j ) = 1 S i S j c k S i c l S j δ(c k, c l ) Generalize the concept of lowest common ancestor to sets of terms (Pandey et al., ECCB, 2008) Λ(S i, S j ) = λ(c k, c l ) c k S i,c l S j ( ) GΛ(Si,S j ) ρ I (S i, S j ) = I(Λ(S i, S j )) = log 2 G r G Λ(Si,S j ) = is the set of molecules that are c k Λ(S i,s j ) G ck associated Pandey, with Koyutürk, all Grama terms in the MCA set

9 Functional Coherence of Module A set of molecules that participates in the same biological processes or functions sub-network with dense intra-connections and sparse interconnections Each module is associated with set of molecular entities, and each molecule associated with set of terms. S 1 = {c 4 }, S 2 = {c 4 }, S 3 = {c 4, c 6 }, S 4 = {c 1, c 6 }, S 5 = {c 1 }, S 6 = {c 6 } Sets: R 1 = {S 1, S 2, S 3, S 4 } R 2 = {S 1, S 2, S 3 } R 3 = {S 3, S 4 }

10 Existing Measure Average (Pu et al., Proteomics, 2007) σ A (R) = 1 n(n 1)/2 Example: σ A (S 1, S 2, S 3, S 4 ) = 1 i<j n ρ(s i, S j ). 1 6 (3 σ A(S 1, S 2, S 3 ) + ρ(s 3, S 4 ) + ρ(s 1, S 4 ) + ρ(s 2, S 4 ))

11 Generalized Information Content Extend the notion of the minimum common ancestor of pairs of terms to tuples of terms λ(c i1,...,c in ) = argmax c n k=1 A ik I(c) σ I (R) = I(Λ(S 1,..., S n )) = log 2 ( GΛ(Si,...,S j ) G r ). where Λ(S 1, S 2,..., S n ) = λ(c i1, c i2,...,c in ) c ij S j,1 j n Example: σ I (S 1, S 2, S 3, S 4 ) = I(r) = 0, no common ancestor!

12 Weighted Information Content Weigh the information content of shared functionality by the number of molecules that contribute to the shared functionality I(c) σ W (R) = 1 1 i n c A i 1 i n c A i I(c) σ W (S 1, S 2, S 3, S 4 ) = 0.86 σ W (S 1, S 2, S 3 ) = 0.75

13 Accounting for Multiple Paths Is "shortest path" a good measure of network proximity? Multiple alternate paths might indicate stronger functional association In well-studied pathways, redundancy is shown to play an important role in robustness & adaptation (e.g., genetic buffering)

14 Random walks with restarts Consider a random walker that starts on a source node s. At every tick, the walker chooses randomly among available edges or goes back to node s with probability c.

15 Proximity Based On Random Walks Simulate an infinite random walk with random restarts at protein i Proximity between proteins i and j is given by the relative amount of time spent at protein j Φ(0) = I, Φ(t + 1) = (1 c)aφ(t) + ci, Φ = lim t Φ(t) Φ(i, j): Network proximity between protein i and protein j A: Stochastic matrix derived from the adjacency matrix of the network I: Identity matrix c: Restart probability Define proximity between proteins i and j as {Φ(i, j) + Φ(j, i)}/2

16 Network Proximity & Functional Similarity Correlation between functional similarity and network proximity

17 normalized average semantic similarity Topological Proximity and Functional Similarity ST DDI Comp-2 DDI S. pombe PPI S. cere PPI -1 x >1/2 4 1/2 4 > x >1/2 8 1/2 8 > x >1/2 12 1/2 12 > x >0 random walk proximity (a) normalized average semantic similarity ST DDI Comp-2 DDI S. pombe PPI S. cere PPI network distance (b) Comparison of the DDI and PPI networks with respect to the relation between semantic similarity vs proximity and network distance

18 Comparison of Coherence Meaures 5 Avg. pairwise term sim. Avg. pairwise molecule sim. generalized IC weighted IC pvalue < 0.05 index of detectability complex set size Index of Dectectability vs. complex sizes mean d(σ) = t T (σ(t)) mean t C (σ(t)) ((stdt T (σ(t))) 2 +(std t C (σ(t))) 2 )/2

19 Conclusion & Ongoing work Random walk based measures of topological proximity are better suited to existing interaction data Measures that quantify coherence among entire sets are superior to aggregares of known pair-wise measures Future work : Using proximity measure to identify disease implicated genes in networks